Water is a fascinating material. Its composition is simple—one oxygen andtwo hydrogen atoms—but its chemistry and physics are extremely complex andexhibit 75 documented anomalies. Although these anomalies and theirmolecular origin are not completely understood, we know that hydrogen bondsplay key roles in all of the phases of water. Moreover, there isexperimental evidence that the polymorphism of the ice structure extendsinto the liquid phase and is associated with a liquid-liquid coexistenceline. This is currently a topic of great interest in water research becausethere are indications that the end point of the coexistence line correspondsto a second critical point inside the supercooled liquid regime. We examinethe recent progress in understanding water anomalies and the liquid-liquidphase transition hypothesis, including the results of recent experimentalwork and molecular simulations of both bulk and confined water. We examineexperimental results that test whether the behavior of liquid water isconsistent with the textquotedblleft liquid polymorphismtextquotedblrighthypothesis that liquid water can exist in two distinct phases of differingdensities. We also examine recent research on the anomalies of nanoconfinedwater and, in particular, on water in biological environments. We find thatthe concept of liquid polymorphism can also describe the properties of otherliquids that have two characteristic length scales.